Phase-step calibration technique based on a two-run-times-two-frame phase-shift method

Xianghong Zhong

doi:10.1364/AO.45.008863

Applied Optics
Vol. 45,
Issue 35,
pp. 8863-8869
(2006)
•https://doi.org/10.1364/AO.45.008863

Phase-step calibration technique based on a two-run-times-two-frame phase-shift method

Xianghong Zhong

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Xianghong Zhong, "Phase-step calibration technique based on a two-run-times-two-frame phase-shift method," Appl. Opt. 45, 8863-8869 (2006)

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Abstract

A novel phase-step calibration technique is presented on the basis of a two-run-times-two-frame phase-shift method. First the symmetry factor M is defined to describe the distribution property of the distorted phase due to phase-shifter miscalibration; then the phase-step calibration technique, in which two sets of two interferograms with a straight fringe pattern are recorded and the phase step is obtained by calculating M of the wrapped phase map, is developed. With this technique, a good mirror is required, but no uniform illumination is needed and no complex mathematical operation is involved. This technique can be carried out in situ and is applicable to any phase shifter, whether linear or nonlinear.

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Equations (15)

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β (rad)	M	β (rad)	M	β (rad)	M	β (rad)	M	β (rad)	M	β (rad)	M
0.10	−0.033	0.35	−0.125	0.60	−0.236	0.85	−0.371	1.10	−0.539	1.35	−0.754
0.11	−0.036	0.36	−0.129	0.61	−0.241	0.86	−0.377	1.11	−0.546	1.36	−0.763
0.12	−0.040	0.37	−0.134	0.62	−0.246	0.87	−0.383	1.12	−0.554	1.37	−0.773
0.13	−0.043	0.38	−0.138	0.63	−0.251	0.88	−0.389	1.13	−0.562	1.38	−0.783
0.14	−0.047	0.39	−0.142	0.64	−0.256	0.89	−0.395	1.14	−0.570	1.39	−0.794
0.15	−0.050	0.4	−0.146	0.65	−0.261	0.90	−0.402	1.15	−0.577	1.40	−0.804
0.16	−0.054	0.41	−0.150	0.66	−0.266	0.91	−0.408	1.16	−0.585	1.41	−0.814
0.17	−0.057	0.42	−0.154	0.67	−0.271	0.92	−0.414	1.17	−0.593	1.42	−0.825
0.18	−0.061	0.43	−0.159	0.68	−0.276	0.93	−0.421	1.18	−0.602	1.43	−0.836
0.19	−0.064	0.44	−0.163	0.69	−0.281	0.94	−0.427	1.19	−0.610	1.44	−0.846
0.20	−0.068	0.45	−0.167	0.70	−0.287	0.95	−0.434	1.20	−0.618	1.45	−0.857
0.21	−0.072	0.46	−0.172	0.71	−0.292	0.96	−0.440	1.21	−0.626	1.46	−0.868
0.22	−0.075	0.47	−0.176	0.72	−0.297	0.97	−0.447	1.22	−0.635	1.47	−0.879
0.23	−0.079	0.48	−0.180	0.73	−0.303	0.98	−0.453	1.23	−0.643	1.48	−0.891
0.24	−0.083	0.49	−0.185	0.74	−0.308	0.99	−0.460	1.24	−0.652	1.49	−0.902
0.25	−0.087	0.50	−0.189	0.75	−0.314	1.00	−0.467	1.25	−0.661	1.50	−0.914
0.26	−0.090	0.51	−0.194	0.76	−0.319	1.01	−0.474	1.26	−0.670	1.51	−0.926
0.27	−0.094	0.52	−0.198	0.77	−0.325	1.02	−0.481	1.27	−0.679	1.52	−0.937
0.28	−0.098	0.53	−0.203	0.78	−0.330	1.03	−0.488	1.28	−0.688	1.53	−0.949
0.29	−0.102	0.54	−0.208	0.79	−0.336	1.04	−0.495	1.29	−0.697	1.54	−0.962
0.30	−0.106	0.55	−0.212	0.80	−0.342	1.05	−0.502	1.30	−0.706	1.55	−0.974
0.31	−0.110	0.56	−0.217	0.81	−0.347	1.06	−0.509	1.31	−0.715	1.56	−0.986
0.32	−0.113	0.57	−0.222	0.82	−0.353	1.07	−0.517	1.32	−0.725	1.57	−0.999
0.33	−0.117	0.58	−0.226	0.83	−0.359	1.08	−0.524	1.33	−0.734
0.34	−0.121	0.59	−0.231	0.84	−0.365	1.09	−0.531	1.34	−0.744

Data	Formula	M1	M2	M3	Mean	Calibration Result (rad)	Real Phase Step (rad)	Error (rad)
Fig. 7(a)	Eq. (7)	−0.791	−0.729	−0.739	−0.753	1.350	1.4	0.050
Fig. 7(b)	Eq. (7)	−0.777	−0.798	−0.792	−0.789	1.386	1.4	0.014
Fig. 7(b)	Eq. (8)	−0.788	−0.806	−0.799	−0.798	1.394	1.4	0.006

β (rad)	M	β (rad)	M	β (rad)	M	β (rad)	M	β (rad)	M	β (rad)	M
0.10	−0.033	0.35	−0.125	0.60	−0.236	0.85	−0.371	1.10	−0.539	1.35	−0.754
0.11	−0.036	0.36	−0.129	0.61	−0.241	0.86	−0.377	1.11	−0.546	1.36	−0.763
0.12	−0.040	0.37	−0.134	0.62	−0.246	0.87	−0.383	1.12	−0.554	1.37	−0.773
0.13	−0.043	0.38	−0.138	0.63	−0.251	0.88	−0.389	1.13	−0.562	1.38	−0.783
0.14	−0.047	0.39	−0.142	0.64	−0.256	0.89	−0.395	1.14	−0.570	1.39	−0.794
0.15	−0.050	0.4	−0.146	0.65	−0.261	0.90	−0.402	1.15	−0.577	1.40	−0.804
0.16	−0.054	0.41	−0.150	0.66	−0.266	0.91	−0.408	1.16	−0.585	1.41	−0.814
0.17	−0.057	0.42	−0.154	0.67	−0.271	0.92	−0.414	1.17	−0.593	1.42	−0.825
0.18	−0.061	0.43	−0.159	0.68	−0.276	0.93	−0.421	1.18	−0.602	1.43	−0.836
0.19	−0.064	0.44	−0.163	0.69	−0.281	0.94	−0.427	1.19	−0.610	1.44	−0.846
0.20	−0.068	0.45	−0.167	0.70	−0.287	0.95	−0.434	1.20	−0.618	1.45	−0.857
0.21	−0.072	0.46	−0.172	0.71	−0.292	0.96	−0.440	1.21	−0.626	1.46	−0.868
0.22	−0.075	0.47	−0.176	0.72	−0.297	0.97	−0.447	1.22	−0.635	1.47	−0.879
0.23	−0.079	0.48	−0.180	0.73	−0.303	0.98	−0.453	1.23	−0.643	1.48	−0.891
0.24	−0.083	0.49	−0.185	0.74	−0.308	0.99	−0.460	1.24	−0.652	1.49	−0.902
0.25	−0.087	0.50	−0.189	0.75	−0.314	1.00	−0.467	1.25	−0.661	1.50	−0.914
0.26	−0.090	0.51	−0.194	0.76	−0.319	1.01	−0.474	1.26	−0.670	1.51	−0.926
0.27	−0.094	0.52	−0.198	0.77	−0.325	1.02	−0.481	1.27	−0.679	1.52	−0.937
0.28	−0.098	0.53	−0.203	0.78	−0.330	1.03	−0.488	1.28	−0.688	1.53	−0.949
0.29	−0.102	0.54	−0.208	0.79	−0.336	1.04	−0.495	1.29	−0.697	1.54	−0.962
0.30	−0.106	0.55	−0.212	0.80	−0.342	1.05	−0.502	1.30	−0.706	1.55	−0.974
0.31	−0.110	0.56	−0.217	0.81	−0.347	1.06	−0.509	1.31	−0.715	1.56	−0.986
0.32	−0.113	0.57	−0.222	0.82	−0.353	1.07	−0.517	1.32	−0.725	1.57	−0.999
0.33	−0.117	0.58	−0.226	0.83	−0.359	1.08	−0.524	1.33	−0.734
0.34	−0.121	0.59	−0.231	0.84	−0.365	1.09	−0.531	1.34	−0.744

Data	Formula	M1	M2	M3	Mean	Calibration Result (rad)	Real Phase Step (rad)	Error (rad)
Fig. 7(a)	Eq. (7)	−0.791	−0.729	−0.739	−0.753	1.350	1.4	0.050
Fig. 7(b)	Eq. (7)	−0.777	−0.798	−0.792	−0.789	1.386	1.4	0.014
Fig. 7(b)	Eq. (8)	−0.788	−0.806	−0.799	−0.798	1.394	1.4	0.006

Abstract

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Figures (7)

Tables (2)

Equations (15)

Applied Optics